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Approximation of delay stochastic equations with constant retardation by usual Ito equations. (English) Zbl 0687.60059

Consider the following system of delay stochastic equations

(1)dx(t)=f(t,x(t),x(t-h))dt+g(t,x(t),x(t-h))dw(t)

with the initial conditions

x(t 0 )=η,x(t 0 +θ)=ϕ(θ),-hθ<0,

where f,g are Lipschitz and satisfy the growth condition, w is Brownian motion, η is a random variable and ϕ is a stochastic process.

By using an approximation result for deterministic hereditary equations by ordinary differential equations, an analogous result is obtained for (1) with the help of Itô equations.

Reviewer: C.Tudor
MSC:
60H20Stochastic integral equations